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Nowadays, industrial systems deal with a wide range of constraints. Output saturation and lack of system model are two types of these constraints. In this paper, a Data-Driven Adaptive Predictive Control (DDAPC) is propounded for a family of unknown non-linear systems featuring output saturation. The design of the control signal only dependent on the input and output data of the system. In this regard, a new adaptive predictive control scheme is suggested using the new developed dynamic linearization model. The stability analysis of the proposed method is provided by proving the boundedness of the tracking error for both time varying and constant desired reference signal and considering the output saturation data, which is a common physical constraint in industrial systems. Furthermore, the proposed method is more robust against the model uncertainties and nonlinearities, in comparison with the common model-based adaptive methods, since its controller design procedures as well as the stability analysis are independent of plant model. To verify the efficiency and applicability of the suggested approach some applicational and numerical simulation examples are provided.